The end-to-end Quality of Service (QoS) control is one of the key factors to the success of next generation networks. Therefore, this paper presents a session-aware QoS mapping and adaptation mechanism that maps the session QoS requirements into the most suitable network service class across heterogeneous mobile networks as well as it adapts the session to the current network conditions. The proposed scheme allows mobile operators to keep network internals sufficiently opaque and to reduce operational costs by mapping and/or adapting sessions to groups of heterogeneous mobile users. Concurrently, the proposed scheme assures acceptable quality levels to on-going sessions, independently of the movement of users. In addition, an experimental evaluation in a QoS mobile multicast environment is presented.